Exam 12: Recursion

The following method correctly adds two ints, returning their sum: public int add(int a, int b) { return (b > 0) ? add(a+1, b-1) : a; }

For the questions below, recall the Towers of Hanoi recursive solution. -The solution to the Towers of Hanoi has a(n) ________ complexity.

A recursive method without a base case leads to infinite recursion.

An infinite loop and an infinite recursion

The following drawing is a line using the Koch snowflake design where order = 2. Show how it would appear with order = 3.

Which of the following recursive methods would execute approximately log ₂ n times for an initial parameter n?

Assume a function g(x) is defined as follows where x is an int parameter: g(x) = g(x - 1) * g (x - 3) if x is even and x > 3 = g(x - 2) if x is odd and x > 3 = x otherwise Write a recursive method to compute g.

Each time the order of a Koch fractal increases by one, the number of straight line segments

The following method recognizes whether a String parameter consists of a specific pattern and returns True if the String has that pattern, false otherwise. Use this recursive method to answer the questions below. public boolean patternRecognizer(String a) { if (a == null) return false; else if (a.length( ) = = 1 | | (a.length( ) = = 2 && a.charAt(0) = = a.charAt(1) ) ) return True; else if (a.length( ) = = 2 && a.charAt(0) != a.charAt(1) ) return false; else if (a.charAt(0) == a.charAt(a.length( ) - 1)) return patternRecognizer(a.substring(1, a.length( ) - 1)); else return false; } -Aside from writing recursive methods, another way that recursion is often used is to define

The following method recognizes whether a String parameter consists of a specific pattern and returns True if the String has that pattern, false otherwise. Use this recursive method to answer the questions below. public boolean patternRecognizer(String a) { if (a == null) return false; else if (a.length( ) = = 1 | | (a.length( ) = = 2 && a.charAt(0) = = a.charAt(1) ) ) return True; else if (a.length( ) = = 2 && a.charAt(0) != a.charAt(1) ) return false; else if (a.charAt(0) == a.charAt(a.length( ) - 1)) return patternRecognizer(a.substring(1, a.length( ) - 1)); else return false; } -If the method is called as patternRecognizer(x) where x is "aa", what will the result be?

The following method recognizes whether a String parameter consists of a specific pattern and returns True if the String has that pattern, false otherwise. Use this recursive method to answer the questions below. public boolean patternRecognizer(String a) { if (a == null) return false; else if (a.length( ) = = 1 | | (a.length( ) = = 2 && a.charAt(0) = = a.charAt(1) ) ) return True; else if (a.length( ) = = 2 && a.charAt(0) != a.charAt(1) ) return false; else if (a.charAt(0) == a.charAt(a.length( ) - 1)) return patternRecognizer(a.substring(1, a.length( ) - 1)); else return false; } -If the statement a.substring(1, a.length( ) - 1) were changed to be (a.substring(1, a.length( )), then the method would

For the questions below, use the following recursive method. public int question1_2(int x, int y) { if (x == y) return 0; else return question1_2(x-1, y) + 1; } -If the method is called as question1_2(8, 3), what is returned?

Traversing a maze is much easier to do iteratively than recursively.

Rewrite the following iterative method as a recursive method that computes the same thing. NOTE: your recursive method will require an extra parameter. public int iterative1(int x) { int count = 0, factor = 2; while (factor < x) { if (x % factor = = 0) count++; factor++; } return count; }

The Koch snowflake has an infinitely long perimeter, but it contains a finite area.

Consider the following recursive sum method: public int sum(int x) { if (x = = 0) return 0; else return sum(x - 1) + 1; } If the base case is replaced with "if (x = = 1) return 1;" the method will still compute the same thing.

Since iterative solutions often use loop variables and recursive solutions do not, the recursive solution is usually more memory efficient (uses less memory) than the equivalent iterative solution.

For the questions below, refer to the following recursive factorial method. public int factorial(int x) { if (x > 1) return x * factorial (x - 1); else return 1; } -How many times is the factorial method invoked if originally called with factorial(5)? Include the original method call in your counting.

Assume page is a Graphics object. If the following method is called with drawIt(50, page), show what is displayed on the Graphics object page. public void drawIt(int x, Graphics page) { if (x > 10) { page.setColor(Color.black); page.drawRect(0, 0, x, x); drawIt(x - 10, page); } }

For the questions below, assume that int[ ] a = {6, 2, 4, 6, 2, 1, 6, 2, 5} and consider the two recursive methods below foo and bar. public int foo(int[ ] a, int b, int j) { if (j < a.length) if (a[j] != b) return foo (a, b, j+1); else return foo (a, b, j+1) + 1; else return 0; } public int bar(int[ ] a, int j) { if (j < a.length) return a[I] + bar(a, j+1); else return 0; } -What is the result of bar(a, 8);?